Find x and y to three significant digits using the formula s = r? (? in radians). $$\begin{array} { | c | c | c | }
\hline \text { Radius, } r & \text { Angle, } \Theta & \text { Distance, } s \
\hline 12 \mathrm {~cm} & 55 ^ { \circ } & x \mathrm {~cm} \
\hline 16 \mathrm {~mm} & 70 ^ { \circ } & y \mathrm {~mm} \
\hline
\end{array}$$
A) x = 3.667; y = 6.222
B) x = 11.519; y = 19.548
C) x = 36.189; y = 61.411
D) x = 115.192; y = 195.477
E) x = 36.189; y = 6.222

Question

Find x and y to three significant digits using the formula s = r? (? in radians).   $$\begin{array} { | c | c | c | } 
\hline \text { Radius, } r & \text { Angle, } \Theta & \text { Distance, } s \
\hline 12 \mathrm {~cm} & 55 ^ { \circ } & x \mathrm {~cm} \
\hline 16 \mathrm {~mm} & 70 ^ { \circ } & y \mathrm {~mm} \
\hline
\end{array}$$
A) x = 3.667; y = 6.222
B) x = 11.519; y = 19.548
C) x = 36.189; y = 61.411
D) x = 115.192; y = 195.477
E) x = 36.189; y = 6.222

Quizplus · Accepted Answer

To convert degrees to radians, we use the formula: 
$\Theta_{	ext{rad}} = \frac{\Theta_{	ext{deg}}\pi}{180}$

For the first case: 
$\Theta_{	ext{rad}} = \frac{55\pi}{180} \approx 0.9599$
$s = r\Theta_{	ext{rad}} = (12)(0.9599) \approx 11.519$

For the second case: 
$\Theta_{	ext{rad}} = \frac{70\pi}{180} \approx 1.2217$
$s = r\Theta_{	ext{rad}} = (16)(1.2217) \approx 19.548$

Therefore, the answer is B.

Find X and Y to Three Significant Digits Using the Formula